12-12-2017 | Harry Millwater: A New Finite Element Method Based on Hypercomplex Algebra for the Computation of High-Order Derivatives

Title: High Performance Computing Incubator Speaker Series:  A New Finite Element Method based on Hypercomplex Algebra for the Computation of High-order Derivatives

Speaker: Dr. Harry Millwater, Professor, Mechanical Engineering, University of Texas at San Antonio

Date: Tuesday, December 12, 2017

Time: 1:30pm-2:30pm

Location: NASA/LaRC, Building 2102, Room 262

Sponsor: Ed Glaessgen, NASA/LaRC

Abstract: The hypercomplex finite element method, ZFEM, is an extension of the traditional finite element methodto hypercomplex algebras. The advantage of the method is that highly accurate arbitrary-order derivativescan be obtained with respect to shape, material or loading parameters as a direct output of the analysis.The key concept is the introduction of imaginary nodal coordinates, which are used to perturb thegeometry and to store the derivatives.

Particular versions of ZFEM and their capabilities include: complex – first order derivative, quaternionsoctonions – 3 & 7 first order derivatives, bicomplex/bidual – 2nd order derivative, tricomplex/tridual –3rd order derivative, etc. The method is general and can be applied in fluid mechanics, heat transfer,structural dynamics, solid mechanics etc.

The hypercomplex finite element method has been implemented as a user element within the Abaquscommercial finite element program. The method is general but has natural applications in fracturemechanics in that the energy release rate can be computed simply and with high accuracy, obviating the need to compute the J integral, for both linear and nonlinear materials. Applications to thermo-elasticity,plasticity, linear elastic, thermal, elasto-plastic, and progressive fracture will be presented.Computational implementation and solution methods will be discussed.

Bio: Dr. Harry Millwater is the Samuel G. Dawson Professor of Mechanical Engineering at the University of Texas at San Antonio. He has 30 years of experience in structural reliability methods. He has prior experience developing the Nessus and Darwin probabilistic codes. Currently he leads the development of the probabilistic airframe risk assessment codes, Smart|LD & Smart|DT, for the FAA. He is the originator of the hypercomplex finite element method under funding from AFRL, AFOSR, ONR, and DoD. He will present a seminar on A New Finite Element Method based on Hypercomplex Algebra for the Computation of High-order Derivatives.